Talk:Interior product

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[edit] Not the right map?

The definition given for interior product is

i_v\omega(u_1,\ldots,u_{p-1})=\omega(v,u_1,\ldots,u_{p-1}).

but the thing on the RHS is not a (p-1)-form! Shouldn't it be

i_v\omega(u_1,\ldots,u_{p-1})=\omega(v,u_2,\ldots,u_{p-1}).

? I'm going to change it... feel free to correct me if I'm wrong. Trevorgoodchild 20:10, 1 March 2007 (UTC)

Thanks for pointing out how unclear this article is: however, ω is a p-form, so that ivω is a (p-1)-form, so the formula was correct. I'll try and rephrase it to make it a bit clearer. Geometry guy 20:40, 1 March 2007 (UTC)


Ok, my mistake. I wonder, though, if there's a way to put the p-form on the LHS and the (p-1)-form on the RHS so that the definition matches the direction of the mapping. I.e., something like this but less ugly:
i_v\left(\omega(u_1,\ldots,u_{p})\right)=(i_v\omega)(v,u_2,\ldots,u_{p}) Trevorgoodchild 11:50, 2 March 2007 (UTC)
Well, you could write
i_v\left(\omega(\cdot,u_2,\ldots,u_{p})\right)=(i_v\omega)(u_2,\ldots,u_{p})
but I'm not sure it is very helpful. Definitions don't usually match the direction of the mapping, e.g., y=f(x) defines y as a function of x, but the direction of the mapping f is from the set of xs to set of ys. Geometry guy 12:09, 2 March 2007 (UTC)
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